AoPSWiki

Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.

Personal tools

Log in

Search

Toolbox

Triangular number

From AoPSWiki

The triangular numbers are the numbers $\displaystyle T_n$ which are the sum of the first $\displaystyle n$ natural numbers from $\displaystyle 1$ to $\displaystyle n$ .

Using the sum of an arithmetic series formula, a formula can be calculated for $\displaystyle T_n$ :

$T_n = \displaystyle\sum_{k=1}^{n}k = 1 + 2 + \ldots + n = \frac{n(n+1)}2$

The rather simple recursive definition can be easily found by noting that $\displaystyle T_{n} = 1 + 2 + \ldots + (n-1) + n = (1 + 2 + \ldots + n-1) + n = T_{n-1} + n$ .

This article is a stub. Help us out by expanding it.

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/Triangular_number"

Category: Stubs

Do you have what it takes to be the next brilliant trader, researcher, or developer at Jane Street Capital? Find out in the Careers in Mathematics Forum.

© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us